60 lakhs = salary (employee) or fee (consultant)?

Rs. 60 lacs would be the CTC. You will have to look at the payslip giving details of its parts such as basic, DA, allowances, perquisites, EPF, PT, etc. 

Tax on salary of 60 lacs is Rs. 16.78 lacs. So Rs. 1.3 lacs will be deducted as TDS each month. First check the break-up of the CTC and then compute your taxable income. Some allowances are exempt.

But if it is professional fees, then TDS will be deducted at 10% or Rs. 6 lacs will be your tax credit at the end of the year. The remaining Rs. 10 lacs or less will have to be paid by you as advance tax. But you may also be eligible to claim expenses as you will be required to file ITR-4.